Find the force exerted by the water on a $2 {\mathrm{m}}^2$ plane surface of a large stone placed at the bottom of a sea $500 \mathrm{m}$ deep. Does the force depend on the orientation of the surface? Neglect the size of the stone in comparison to the depth of the sea.

Water is filled in a rectangular tank of size $3 \mathrm{m}\times 2 \mathrm{m}\times 1 \mathrm{m}$.

$\left(a\right)$ Find the total force exerted by the water on the bottom surface of the tank.

$\left(b\right)$ Consider a vertical side of area $2 \mathrm{m}\times 1 \mathrm{m}$. Take a horizontal strip of width $\delta x$ $\mathrm{m}$ in this side, situated at a depth of $x$ $\mathrm{m}$ from the surface of the water. Find the force by the water on this strip.

$\left(c\right)$ Find the torque of the force calculated in part $\left(b\right)$ about the bottom edge of this side.
$\left(d\right)$ Find the total force by the water on this side.
$\left(e\right)$ Find the total torque by the water on the side about the bottom edge. Neglect the atmospheric pressure and take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A cube of ice floats partly in water and partly in $K.\mathrm{oil}$. Find the ratio of the volume of ice immersed in water to that in $K.\mathrm{oil}$. The specific gravity of K.oil is $0.8$ and that of ice is $0.9$.

​​​​​​​